• Structural Engineering and Mechanics
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• v.24 no.4
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• pp.395-410
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• 2006

This paper reports the result of an investigation into wave propagation in orthotropic laminated piezoelectric cylindrical shells in hydrothermal environment. A dynamic model of laminated piezoelectric cylindrical shell is derived based on Cooper-Naghdi shell theory considering the effects of transverse shear and rotary inertia. The wave characteristics curves are obtained by solving an eigenvalue problem. The effects of layer numbers, thickness of piezoelectric layers, thermal loads and humid loads on the wave characteristics curves are discussed through numerical results. The solving method presented in the paper is validated by the solution of a classical elastic shell non-containing the effects of transverse shear and rotary inertia. The new features of the wave propagation in laminated piezoelectric cylindrical shells with various laminated material, layer numbers and thickness in hydrothermal environment and some meaningful and interesting results in this paper are helpful for the application and the design of the ultrasonic inspection techniques and structural health monitoring.

• The Journal of the Acoustical Society of Korea
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• v.31 no.6
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• pp.399-409
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• 2012

In this paper we propose a method for measuring the shear modulus of an ultrasound soft tissue phantom using an acoustic radiation force. The proposed method quantitatively determines the shear modulus based on the rise time of a displacement induced by an acoustic radiation force at the focal point of a focused ultrasound beam. The shear wave speed and shear modulus obtained from the proposed method and a shear wave propagation method were compared to verify the validity of the proposed method. In the shear wave propagation method, the shear modulus is first computed by measuring the propagating speed of a shear wave induced in a phantom by a limited-diffraction transmit field, and then was compared to that obtained with the proposed method in an ultrasound data acquisition system calibrated based on the first computed shear modulus. The relative errors between the two methods were found to be 4% for shear wave speed and less than 9% for shear modulus, confirming the usefulness of the proposed method.

• Geomechanics and Engineering
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• v.33 no.4
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• pp.381-391
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• 2023

The aim of this work is to analyze and predict the wave propagation behavior of the carbon nanotube reinforced composites (CNTRC) beams within the framework of various higher order shear deformation beam theory. Using the Euler-Lagrange principle, the wave equations for CNTRC beams are derived, where the determining factor is to make the determinant equal to zero. Based on the eigenvalue method, the relationship between wave number and circular frequency is obtained. Furthermore, the phase and group velocities during wave propagation are obtained as a function of wave number, and the material properties of CNTRC beams are estimated by the mixture rule. In this paper, various higher order shear beam theory including Euler beam theory, Timoshenko beam theory and other beam theories are mainly adopted to analyze the wave propagation problem of the CNTRC beams, and by this way, we conduct a comparative analysis to verify the correctness of this paper. The mathematical model provided in this paper is verified numerically by comparing it with some existing results. We further investigate the effects of different enhancement modes of CNTs, volume fraction of CNTs, spring factor and other aspects on the wave propagation behaviors of the CNTRC beams.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.12
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• pp.3369-3376
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• 1994

A finite element program for elastic stress wave propagation is developed in order to investigate the shape of stress field and analysis the magnitude of stress wave intensity at time increment. Accuracy and reliance of the finite element analysis are acquired when the element size is smaller than the product of the stress wave speed and the critical value of increasing time step. In the finite element analysis and theoretical solution, the longitudinal stress wave is propagated to the similar direction of impact load, and the stress wave intensity is expressed in terms of the ratio of propagated area. The direction of shear wave is declined at an angle of 45 degrees compared with longitudinal stress wave and the speed of shear wave is half of the longitudinal stress wave.

• Earthquakes and Structures
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• v.26 no.2
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• pp.163-174
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• 2024

Dynamic equilibrium equations for finite element analysis were derived for the free field one-dimensional shear wave propagation through the horizontally layered soil deposits with the elastic half-space. We expressed Rayleigh's viscous damping consisting of mass and stiffness proportional terms. We considered two cases where damping matrices are defined in the total and relative displacement fields. Two forms of equilibrium equations are presented; one in terms of total motions and the other in terms of relative motions. To evaluate the performance of new equilibrium equations, we conducted two sets of site response analyses and directly compared them with the exact closed-form frequency domain solution. Results show that the base shear force as earthquake load represents the simpler form of equilibrium equation to be used for the finite element method. Conventional finite element procedure using base acceleration as earthquake load predicts exact solution reasonably well even in soil deposits with unrealistically high damping.

• Proceedings of the KSR Conference
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• 2011.10a
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• pp.2650-2652
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• 2011

The fiber reinforced composite materials have many advantages due to their high strength-to-density ratios. Thus they have been widely used in many industrial applications. As the wave propagation are closely related to dynamic analysis of structures, it is very important to predict them. This paper presents a wave propagation in the axially loaded axial-bending-shear coupled composite laminated beams which are represented by the Timoshenko beam models based on the first-order shear deformation theory.

• Structural Engineering and Mechanics
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• v.76 no.4
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• pp.551-559
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• 2020

On the basis of nonlocal strain gradient theory, considering the material properties of porous FGM changing with thickness and the influence of moment of inertia, the wave equation of FG nano circular plate is derived by using the first-order shear deformation plate theory, by introducing dimensionless parameters, we transform the equations into dimensionless wave equations, and the dispersion relations of bending wave, shear wave and longitudinal wave are obtained by Laplace and Hankel integral transformation method. The influence of nonlocal parameter, porosity volume fraction, strain gradient parameters and power law index on the propagation characteristics of bending wave, shear wave and longitudinal wave in FG nano circular plate.

• Structural Engineering and Mechanics
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• v.57 no.5
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• pp.837-859
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• 2016

An efficient shear deformation theory is developed for wave propagation analysis of an infinite functionally graded plate in the presence of thermal environments. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The thermal effects and temperature-dependent material properties are both taken into account. The temperature field is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching.bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and temperature on wave propagation of functionally graded plate are discussed in detail. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded plate. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

• Steel and Composite Structures
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• v.37 no.1
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• pp.27-35
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• 2020

This study examines the wave propagation of the functionally graded polymer composite (FG-PC) nanoplates reinforced with graphene nanoplatelets (GNPs) resting on elastic foundations in the framework of the nonlocal strain gradient theory incorporating both stiffness hardening and softening mechanisms of nanostructures. To this end, the material properties are based on the Halpin-Tsai model, and the expressions for the classical and higher-order stresses and strains are consistently derived employing the second-order shear deformation theory. The equations of motion are then consistently derived using Hamilton's principle of variation. These governing equations are solved with the help of Trial function method. Extensive numerical discussions are conducted for wave propagation of the nanoplates and the influences of different parameters, such as the nonlocal parameter, strain gradient parameter, weight fraction of GNPs, uniform and non-uniform distributions of GNPs, elastic foundation parameters as well as wave number.

• Coupled systems mechanics
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• v.13 no.1
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• pp.43-60
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• 2024

This work presents an analytical approach to investigate wave propagation in bi-directional functionally graded cantilever porous beam. The formulations are based on Touratier's higher-order shear deformation beam theory. The physical properties of the porous functionally graded material beam are graded through the width and thickness using a power law distribution. Two porosities models approximating the even and uneven porosity distributions are considered. The governing equations of the wave propagation in the porous functionally graded beam are derived by employing the Hamilton's principle. Closed-form solutions for various parameters and porosity types are obtained, and the numerical results are compared with those available in the literature.The numerical results show the power law index, number of wave, geometrical parameters and porosity distribution models affect the dynamic of the FG beam significantly.